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Browsing by Author "Vavasis, Stephen A."
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Density Graphs and Separators
Miller, Gary L.; Vavasis, Stephen A. (Cornell University, 199011)We propose a class of graphs that would occur naturally in finiteelement problems, and we prove a bound on separators for this class of graphs. For threedimensional graphs, our separator bound is $O(N^{2/3})$. We also ... 
Fast Wavelet Transforms for Matrices Arising from Boundary Element Methods
Bond, David M.; Vavasis, Stephen A. (Cornell University, 199403)(The following contains mathematical formulae and symbols that may become distorted in ASCII text.) For many boundary element methods applied to Laplace's equation in two dimensions, the resulting integral equation has ... 
Nested Dissection for Sparse Nullspace Bases
Stern, Julio M.; Vavasis, Stephen A. (Cornell University, 199012)We propose a nested dissection approach to finding a fundamental cycle basis in a planar graph. the cycle basis corresponds to a fundamental nullspace basis of the adjacency matrix. This problem is meant to model sparse ... 
A Note on Wavelet Bases for TwoDimensional Surfaces
Vavasis, Stephen A. (Cornell University, 199009)Recent work by Beylkin, Coifman and Rokhlin has demonstrated that integral equations for functions on $IR$ can be solved rapidly by expressing the integrands in a wavelet basis. Boundary element methods for solving partial ... 
Numerical Conformal Mapping Using Crossratios and Delaunay Triangulation
Driscoll, Tobin; Vavasis, Stephen A. (Cornell University, 199602)We propose a new algorithm for computing the Riemann mapping of the unit disk to a polygon, also known as the SchwarzChristoffel transformation. The new algorithm, CRDT, is based on crossratios of the prevertices, and ... 
Preconditioning for Boundary Integral Equations (Preliminary Version)
Vavasis, Stephen A. (Cornell University, 199002)We propose new classes of preconditioners for the linear systems arising from a boundary integral equation method. The problem under consideration is Laplace's equation in three dimensions. The system arising in this context ... 
Proving PolynomialTime for SphereConstrained Quadratic Programming
Vavasis, Stephen A.; Zippel, Richard (Cornell University, 199012)Recently Ye and Karmarkar have proposed similar algorithms for minimizing a nonconvex quadratic function on a sphere. These algorithms are based on trustregion work going back to Levenberg and Marquardt. Although both ... 
Quadratic Programming is in NP
Vavasis, Stephen A. (Cornell University, 199002)Quadratic programming is an important example of optimization with applications to engineering design, coombinatorical optimization, game theory, and economics. Garey and Johnson [1979] state that quadratic programming ... 
Quality Mesh Generation in Higher Dimensions
Mitchell, Scott A.; Vavasis, Stephen A. (Cornell University, 199612)We consider the problem of triangulating a ddimensional region. Our mesh generation algorithm, called QMG, is a qradtreebased algorithm that can triangulate any polyhedral region including nonconvexregions with holes. ... 
Quality Mesh Generation in Three Dimensions
Mitchell, Scott A.; Vavasis, Stephen A. (Cornell University, 199202)We show how to triangulate a three dimensional polyhedral region with holes. Our triangulation is optimal in the following two senses: First, our triangulation achieves the best possible aspect ratio up to a constant. ... 
Quality Mesh Generation in Three Dimensions
Mitchell, Scott A.; Vavasis, Stephen A. (Cornell University, 199209)We show how to triangulate a three dimensional polyhedral region with holes. Our triangulation is optimal in the following two senses. First, our triangulation achieves the best possible aspect ratio up to a constant. ... 
Stable Finite Elements for Problems With Wild Coefficients
Vavasis, Stephen A. (Cornell University, 199306)We consider solving an elliptic boundary value problem in the case that the coefficients vary by many orders of magnitude over the domain. A linear finite element method is used. It is shown that the standard method for ... 
Stable Numerical Algorithms for Equilibrium
Vavasis, Stephen A. (Cornell University, 199209)An equilibrium system (also known as a KKT system, a saddle point system, or a sparse tableau) is a square linear system with a certain structure. G. Strang has observed that equilibrium systems arise in optimization, ... 
Stable Numerical Algorithms for Equilibrium Systems
Vavasis, Stephen A. (Cornell University, 199204)An equilibrium system (also known as a KKT system, a saddlepoint system or a sparse tableau) is a square linear system with a certain structure. G. Strang has observed that equilibrium systems arise in optimization, ...